MinT - Information on Result #2681678

Information on Result #2681678

Linear OOA(3²⁰³, 173, F₃, 3, 65) (dual of [(173, 3), 316, 66]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3²⁰⁰, 172, F₃, 3, 65) (dual of [(172, 3), 316, 66]-NRT-code), using

trace code [i] based on linear OOA(9¹⁰⁰, 86, F₉, 3, 65) (dual of [(86, 3), 158, 66]-NRT-code), using
- constructionÂ X applied to AG(3;F,165P) âŠ‚ AG(3;F,179P) [i] based on
  1. linear OOA(9⁸⁷, 77, F₉, 3, 65) (dual of [(77, 3), 144, 66]-NRT-code), using algebraic-geometric NRT-code AG(3;F,165P) [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]
  2. linear OOA(9⁷³, 77, F₉, 3, 51) (dual of [(77, 3), 158, 52]-NRT-code), using algebraic-geometric NRT-code AG(3;F,179P) [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78 (see above)
  3. linear OOA(9¹³, 9, F₉, 3, 13) (dual of [(9, 3), 14, 14]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;14,9) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.